Period Mapping at Infinity

Show simple item record Griffiths, Phillip 2020-05-07T12:41:07Z 2020-05-07T12:41:07Z 2020-05-06
dc.description IMSA talk on 5/6/20. Based on joint work in progress with Mark Green and Colleen Robles. en_US
dc.description.abstract Hodge theory provides a basic invariant of complex algebraic varieties. For algebraic families of smooth varieties the global study of the Hodge structure on the cohomology of the varieties (period mapping) is a much studied and rich subject. When one completes a family to include singular varieties the local study of how the Hodge structures degenerate to limiting mixed Hodge structures is also much studied and very rich. However, the global study of the period mapping at infinity has not been similarly developed. This has now been at least partially done and will be the topic of this talk. Sample applications include: new global invariants of limiting mixed Hodge structures; a generic local Torelli assumption implies that moduli spaces are log canonical (not just log general type); and extension data and asymptotics of the Ricci curvature; a proposed construction of the toroidal compactification of the image of period mapping. The key point is that the extension data associated to a limiting mixed Hodge structure has a rich geometric structure and this provides a new tool for the study of families of singular varieties in the boundary of families of smooth varieties. en_US
dc.language.iso en_US en_US
dc.subject period mappings en_US
dc.subject Hodge Theory en_US
dc.subject Hodge structures en_US
dc.title Period Mapping at Infinity en_US
dc.type Lecture/speech en_US

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